Question

Consider a​ zero-coupon bond with a $1,000 face value and 15 years left until maturity. If the bond is currently trading for $468, then the yield to maturity on this bond is closest​ to:
A. 46.8
B. 53.2
C. 2.6
D. 5.19​

Answer 1

Answer:

D. 5.19

Explanation:

Zero coupon bond is the bond which does not offer any interest payment. It is issued on deep discount price and Traded in the market on discounted price.

According to given data

Face value = F = $1,000

Year to maturity = n = 15 Years

Current price = P = $468

Yield to maturity = [ ( F / P )^(1/15) ] - 1

Yield to maturity = [ ( $1,000 / 468 )^(1/15) ] - 1

Yield to maturity = 1.0519 - 1

Yield to maturity = 0.0519 = 5.19%

Answer 2

Answer:

5.19 ( D )

Explanation:

A zero-coupon bond is a bond traded/issued to the investor at a discounted price i.e a price lower than the actual face value of the bond. this type of bond dose not attract periodic interest payments rather at the time of maturity the initial face value of the bond is paid to the investor.

The  value of a Zero-coupon bond can be calculated as

value of zero - coupon bond = $\frac{F}{( 1 + r )^{t} }$

F = face value

r = yield

t = time

But the yield to maturity can also be calculated using this formula

r = $(\frac{F}{Cp} )^{\frac{1}{T}-1 }$

F = face value of the bond ( $1000 )

Cp = current price ( $468 )

T = time to maturity ( 15 )

therefore yield =  $(\frac{1000}{468} )^{\frac{1}{15}-1 }$

= 2.13675$2^{\frac{1}{15 }-1 }$

= 0.05186 = 5.186

i.e the yield to maturity is closest to 5.19 ( D )